deletions | additions       diff --git a/Asteroseismic Calculations.tex b/Asteroseismic Calculations.tex  index f7cf685..4450cc1 100644  --- a/Asteroseismic Calculations.tex  +++ b/Asteroseismic Calculations.tex 
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%For KEPLER, the sampling rate of the long-cadence mode restricts the sensitivity to frequencies below $\sim 280\mu$Hz (Nyquist frequency).  In order to calculate the splitting of mixed modes we adopted the adiabatic pulsation code ADIPLS \citep[][2011 June release]{JCD:2008}. This code is coupled and distributed within the MESA code suite \citep{Paxton2013}.     We use the MESA calculated profiles (structure and angular velocity) to calculate the kernels and then the resulting splittings.     Rotation is known to lift the degeneracy between the non-radial modes of the same radial order n and degree l but different azimuthal order m. In the case where the rotation of the star is slow enough so that the effects of the centrifugal force can be neglected, a first-order perturbation approximates well the effects of rotation on the mode frequencies.    Assuming a spherically symmetric rotation profile one can write the frequency of the $(n,l,m)$ mode as  \begin{equation}  \nu_{n,l,m}=\nu_{n,l,0}+m\delta\nu_{n,l} 
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Therefore rotational splittings are basically a weighted measure of the star’s rotation rate through the  rotational Kernels.  The expression of rotational splittings for spherically symmetric rotating stars, which is given by Eq. \ref{eq_split_th}, was first obtained by \cite{cowling49} and \cite{ledoux49} (for a review on In order to calculate  the effect splitting  of rotation on the mode frequencies, see e.g. \citealt{goupil11}). We note that Eq. \ref{eq_split_th} implies that mixed modes we adopted  the components of a rotational multiplet are expected to be uniformly spaced by adiabatic pulsation code ADIPLS \citep[][2011 June release]{JCD:2008}. This code is coupled and distributed within  the splitting $\delta\nu_{n,l}$. MESA code suite \citep{Paxton2013}.